?sy(he)ev
计算对称（Hermite）矩阵的所有特征值与特征向量。
接口定义
C Interface：
ssyev_(const char *jobz, const char *uplo, const int *n, float *A, const int *lda, float *w, float *work, const int *lwork, int * info);
dsyev_(const char *jobz, const char *uplo, const int *n, double *A, const int *lda, double *w, double *work, const int *lwork, int * info);
cheev_(const char *jobz, const char *uplo, const int *n, float _Complex *A, const int *lda, float *w, float _Complex *work, const int *lwork, float* rwork, int * info);
zheev_(const char *jobz, const char *uplo, const int *n, double _Complex *A, const int *lda, double *w, double _Complex *work, const int *lwork, double* rwork, int * info);
Fortran Interface：
SSYEV(jobz, uplo, n, a, lda, w, work, lwork, info);
DSYEV(jobz, uplo, n, a, lda, w, work, lwork, info);
CHEEV(jobz, uplo, n, a, lda, w, work, lwork, rwork, info);
ZHEEV(jobz, uplo, n, a, lda, w, work, lwork, rwork, info);
参数
参数 |
类型 |
说明 |
输入/输出 |
|---|---|---|---|
jobz |
字符型 |
|
输入 |
uplo |
字符型 |
|
输入 |
n |
整数型 |
矩阵A的维度，大于或等于0。 |
输入 |
a |
|
|
输入，输出 |
lda |
整数型 |
矩阵A的主维，大于或等于max(1, N)。 |
输入 |
w |
|
Info=0时，以升序存储特征值，长度为N。 |
输出 |
work |
|
Info=0时，work(0)返回最优lwork大小。 |
输出 |
lwork |
整数型 |
work数组的长度。 lwork=-1时查询最优work大小，结果保存在work[0]中。且lwork ≥ max(1, 2*n-1)。 |
输入 |
rwork（复数特有） |
|
工作数组，取值max(1, 3*n-1)。 |
输出 |
info |
整数型 |
状态值：
|
输出 |
依赖
#include "klapack.h"
示例
C Interface：
char jobz = 'V';
char uplo = 'L';
int n = 5;
int lda = 5;
int info = 0;
double w[5];
double *work = NULL;
double qwork;
int lwork = -1;
/*
* Symmetric A (stored in column-major):
* 7.027 8.710 1.015 6.929 7.584
* 8.710 0.839 2.469 3.850 0.559
* 1.015 2.469 1.930 6.761 7.207
* 6.929 3.850 6.761 4.344 4.804
* 7.584 0.559 7.207 4.804 6.177
*/
double a[] = {7.027, 8.710, 1.015, 6.929, 7.584,
8.710, 0.839, 2.469, 3.850, 0.559,
1.015, 2.469, 1.930, 6.761, 7.207,
6.929, 3.850, 6.761, 4.344, 4.804,
7.584, 0.559, 7.207, 4.804, 6.177};
/* Query optimal work size */
dsyev_(&jobz, &uplo, &n, a, &lda, w, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate eigenvalues and eigenvectors */
dsyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, &info);
free(work);
/*
* Output:
* Eigenvalues (in w)
* -1.770722 -0.845606 -0.203058 -5.712058 3.044889
* Eigenvectors (in a, stored in column-major)
* 0.547211 -0.528441 0.339953 -0.172302 -0.531245
* 0.050685 -16.554919 -5.702155 2.261598 15.521155
* -0.456110 0.988485 0.587808 -3.161022 -1.099502
* -0.443428 -1.398420 0.424293 0.800628 0.016423
* -0.541596 -1.770722 -0.845606 -0.203058 -5.712058
*/
Fortran Interface：
CHARACTER :: jobz = "V"
CHARACTER :: uplo = "L"
PARAMETER (n = 5)
PARAMETER (lda = 5)
INTEGER :: info = 0
REAL(8) :: w(5);
REAL(8) :: qwork(1)
REAL(8), ALLOCATABLE :: work(:)
INTEGER :: lwork = -1
* Symmetric A (stored in column-major):
* 7.027 8.710 1.015 6.929 7.584
* 8.710 0.839 2.469 3.850 0.559
* 1.015 2.469 1.930 6.761 7.207
* 6.929 3.850 6.761 4.344 4.804
* 7.584 0.559 7.207 4.804 6.177
REAL(8) :: a(n, n)
DATA a / 7.027, 8.710, 1.015, 6.929, 7.584,
$ 8.710, 0.839, 2.469, 3.850, 0.559,
$ 1.015, 2.469, 1.930, 6.761, 7.207,
$ 6.929, 3.850, 6.761, 4.344, 4.804,
$ 7.584, 0.559, 7.207, 4.804, 6.177 /
* Query optimal work size
EXTERNAL DSYEVD
CALL DSYEV(jobz, uplo, n, a, lda, w, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
* Calculate eigenvalues and eigenvectors
CALL DSYEV(jobz, uplo, n, a, lda, w, work, lwork, info)
DEALLOCATE(work);
* Output:
* Eigenvalues (in w)
* -1.770722 -0.845606 -0.203058 -5.712058 3.044889
* Eigenvectors (in a, stored in column-major)
* 0.547211 -0.528441 0.339953 -0.172302 -0.531245
* 0.050685 -16.554919 -5.702155 2.261598 15.521155
* -0.456110 0.988485 0.587808 -3.161022 -1.099502
* -0.443428 -1.398420 0.424293 0.800628 0.016423
* -0.541596 -1.770722 -0.845606 -0.203058 -5.71205
